A Challenging Question about an Infinite Universe.

[xelasnave]

I have never made it a secret that I don't like the big bang theory.
I don't care what science concludes but how the universe could grow from a speck to all there is, as huge as it is, for me it seems unlikely.
Thought up initially by a priest who presumably believed in God and wanted to give creation a scientific base...but the big bang does not cover the moment of creation but chimes in a split second after leaving open the creation question which one could easily attribute to God.
I really think our cosmology may be driven by philosophy.
Nevertheless this is our best theory.

[xelasnave]

The only alternative theory was the steady state theory which is also difficult to comprehend with it's implication of the universe being timeless with no start in time.
I am not happy with that either.

[sjastro]

A further point on the reference to {1+2+3+4.....}=-1/12 in the book on String Theory by Joseph Polchinski is that the mathematical formalism is based on the operator method.
To save space, equations are truncated to only include the actions of the operator on the quantum states. The quantum states are not included in the equations.

The equation 1.3.32 in the book does not illustrate the summing of the numbers from one to infinity, but the summing of the energy levels of the quantum states which are multiples of (n+1/2), where n=1,2,3........

Steven

[sjastro]

Originally Posted by xelasnave

I have never made it a secret that I don't like the big bang theory.
I don't care what science concludes but how the universe could grow from a speck to all there is, as huge as it is, for me it seems unlikely.
Thought up initially by a priest who presumably believed in God and wanted to give creation a scientific base...but the big bang does not cover the moment of creation but chimes in a split second after leaving open the creation question which one could easily attribute to God.
I really think our cosmology may be driven by philosophy.
Nevertheless this is our best theory.

Alex,

Isaac Newton used the Bible to date the creation of the Universe to around 4,000 BC but this doesn't detract from his work as a scientist.
Interesting how Lemaitre was first and foremost a scientist, but being a priest has somehow muddied the waters.
If Lemaitre wasn't a priest would it have added more credibility to the theory?
Even Albert was initially concerned about a possible covert religious content in the theory but came about to accept it.

Steven

[xelasnave]

Thanks for that Steven.
Yes it would be more acceptable if there were no priests involved.
I don't trust them at all.
Fortunately unlike other crack pots I can nevertheless embrace mainstream.

[Eratosthenes (Peter)]

...in any case it was Friedman who proposed the first expanding universe model (based on GR). Lemaitre's model was proposed later but nevertheless independently (apparently).

Whilst it's true that Georges Lemaitre was a Catholic Priest that dressed the part, he worked as an astronomer, cosmologist and Physics professor. He was by no means some sort of Vatican sponsored Theologian dabbling in cosmology in order to validate the Book of Genesis.

One would assume that Hubble's Constant was calculated and published by Edwin Hubble himself - it wasn't. Lemaitre was the first to derive Hubbles law and also estimate a value for Hubble's constant. The fact that he wore a Catholic frock and white band around his neck is irrelevant - he was one serious Physicist who contributed in a huge way, during a period where the great Physics Icons where doing their great work.

.........some quantum field effects involve negative energy

[xelasnave]

One question I would like help with is if GR was developed, I think but am unsure, when it was thought the Universe was static but it happily described an expanding Universe
I do respect our priest it's good that you stood up for him.

[Eratosthenes (Peter)]

Originally Posted by xelasnave

One question I would like help with is if GR was developed, I think but am unsure, when it was thought the Universe was static but it happily described an expanding Universe
I do respect our priest it's good that you stood up for him.

Not only was the Static model of the Universe the major cosmological paradigm at the time of Einstein's GR theory, Einstein had to input that famous parameter (cosmological constant, Λ) into his GR tensor equations so that the Universe wouldn't expand itself to Smitherenes but rather behave like a static entity. (Einstein's biggest blunder as it turned out)

With the relatively recent discovery that the Universe is not only expanding but the expansion rate is accelerating, (attributed to the mysterious dark Energy repulsion force) that cosmological constant, Λ has made a big come back into Physics and cosmology.

It appears that Einstein himself didn't quite appreciate the ramifications of his Special and General Relativity theories. Einstein initially refused to accept the work of Friedman, Hubble and even fought against the stochastic nature of Quantum mechanics. I recall reading that Einstein had to meet with Edwin Hubble to discuss his red shift measurements and by the time he left, he was convinced that the Universe was indeed expanding.

Cosmology is a fantastic area of Science/Philosophy/mathematics to be involved with professionally, or even as an amateur - there is certainly something deep involved. Its like chasing God around, if you believe in God, trying to corner her and tell her "I know what you did, great work". Or if you are an atheist, there is the equally important search for meaning and understanding.

[xelasnave]

He did not buy the idea of black holes..or so I believe.
You mentioned it started with something the size of an electron.
Lately I get the impression that at the point of singularity it is perhaps not correct to to see it as necessarily a miniscule object.
I wonder have you a view of what it means this singularity.

[xelasnave]

I am an atheist but I am sure god did it.

[xelasnave]

Hubble would have been a powerful and convincing man.
Ex lawyer and I believe he had opportunity to be a heavy weight boxer looking to a world title attempt.
I probably would not argue with him..if he said the universe is expanding I would go along with him...maybe.

[Eratosthenes (Peter)]

Originally Posted by xelasnave

He did not buy the idea of black holes..or so I believe.
You mentioned it started with something the size of an electron.
Lately I get the impression that at the point of singularity it is perhaps not correct to to see it as necessarily a miniscule object.
I wonder have you a view of what it means this singularity.

I agree - I tend to view a singularity in its mathematical context. A point of infinite density and zero size. Its physical significance becomes meaningless, but mathematicians recognise a singularity as an undefined concept/entity.

Plenty of evidence exists that Black Holes are real physical objects in the Universe - whether they "actually" have at their centers, points of infinite space time curvature or density is another matter. It may well be just a very compressed object which creates such a high gravitational field that light itself cannot escape.

Who knows xela

[xelasnave]

If we could make an ingot of dark matter say like a gold bar for example and sat it on the desk would we be able to see it?

[Eratosthenes (Peter)]

we may be able to see some secondary effects caused by this ingot of yours

we certainly would be able to feel it if it is concentrated enough. it is after all pushing outwards...or is it?

on the other hand dark energy may not be acting upon Baryonic matter or 'normal' energy directly or in any way at all.

[xelasnave]

I don't know if it is pushing outwards or what it's doing.
I don't know anything about it other than what I have learned when reading about it.
It seems to me we assume the laws of physics to be universal and our current laws of gravity tell us there should be mass where we do not observe it.
As we can't see it and because we can't explain this situation without more matter than we observe the unseen matter has been called dark matter,
If our gravity laws are valid, and it is somewhat reasonable to expect they are valid then something is interacting gravitationally with matter we can see (stars that are moving faster than our gravity laws predict )
So it is a curious matter.

[xelasnave]

Could dark matter be found in clumps or is dust like.
Could there be clumps as big as a house or even the size of a planet.
Could our gravity laws be questioned given dark matter was not predicted..or was it

[xelasnave]

I think to be fair calling these people such is not fair really.
Mind you in the past I have made similar comments.
However I see this as no more than personal frustration that we still do not know everything.
I think it great there are so many people engaged.
All levels from crank to leading physicist .

[xelasnave]

Sorry Peter I forgot to thank you for your good explanations.

[Eratosthenes (Peter)]

....so the "-1/12" result has units of energy? (ie eV or J)

The ground state energy, ie n=0, is not equal to zero (1/2hώ) and yet the summation in the Polchinski reference is from n=1 to infinity. Is the ground state energy omitted?

The quantum energy states are distinctly separated by an equal energy level equalling hώ, which is a small number, but nevertheless a finite number. So what happens when you sum an infinite number of finite numbers that increase by the same amount?

The negative sign as well as the 1/12 result needs to be physically explained. What exactly does it represent?

[sjastro]

Originally Posted by Eratosthenes

....so the "-1/12" result has units of energy? (ie eV or J)

Neither. The units are in hw where h is Planck's constant and w is the frequency of the oscillator.

The ground state energy, ie n=0, is not equal to zero (1/2hώ) and yet the summation in the Polchinski reference is from n=1 to infinity. Is the ground state energy omitted?

The mathematics behind both Quantum Field Theory and String Theory involves the use of mathematical operators acting on the energy state which brings about a particular change.
One such operator for the Hamiltonian H in equation 1.3.30 involves a general term aⁿₓ. This operator drops the bosonic string into the next lowest energy level.
If you start off with n=0, the operator will drop the string into an n=-1 energy level. But there cannot be an n=-1 level as the ground state exists for n=0. Hence you start from n=1 which also includes the ground state for the string. Note that n=0 is the vacuum state.

The quantum energy states are distinctly separated by an equal energy level equalling hώ, which is a small number, but nevertheless a finite number. So what happens when you sum an infinite number of finite numbers that increase by the same amount?

This has already been explained through renormalization.
The energy levels above a particular level are cut off as they exist above the energy threshold.
This is handled mathematically by multiplying each term in the sum 1.3.31 by an exp(-n) factor. As n becomes larger, the exp(-n) factor becomes smaller. For large n, exp(-n) is approximately zero.
The infinite series is truncated. Remaining terms can be further cancelled out by symmetry leaving 1.3.35 which equals 1.3.31.

The negative sign as well as the 1/12 result needs to be physically explained. What exactly does it represent?

It's been explicitly explained in the reference as.

This finite remainder is an example of a Casimir energy, coming from the fact that the string has a finite length.